[Ga_x2]

Please explain how we can know the distance between LA and New York by looking at the arrival times of airplanes without knowing anything about their speed.

no. Distance. Is. Needed.
Look up proportions in the dictionary.
He's comparing times.
He doesn't give a faq about distance.

[Curious Squirrel]

Once again, no distance is being used here, nor is any being calculated. Just the 'raw' data of flight time.

Please explain how we can know the distance between LA and New York by looking at the arrival times of airplanes without knowing anything about their speed.

We don't care about the distance.
We don't care about the speed of the plane.
All we care about is the average (or perhaps mean depending) time it takes to get from LA to NY by plane.
This can be used as a distance 'replacement' or analogue so long as we simply use the actual times taken.

[TomInAustin]

Once again, no distance is being used here, nor is any being calculated. Just the 'raw' data of flight time.

Please explain how we can know the distance between LA and New York by looking at the arrival times of airplanes without knowing anything about their speed.

We don't care about the distance.
We don't care about the speed of the plane.
All we care about is the average (or perhaps mean depending) time it takes to get from LA to NY by plane.
This can be used as a distance 'replacement' or analogue so long as we simply use the actual times taken.

Are we talking round earth hours?

[3DGeek]

Please tell us the distance between New York and Paris without using a method that assumes the earth is round.

Oh good grief Tom...you really think you can kill the debate with such a ridiculous challenge?   Remember, we're smarter than you are.

In 1878, a 2,242 nautical mile cable was manufactured in England by Siemens Brothers.  The cable was laid in June 1879 between Brest (France) and the island of Saint-Pierre (Newfoundland) by the cable ship "Faraday".

They didn't run out of cable along the way - but history does not recall whether they had any left over.

So we can be quite certain that Brest to Saint-Pierre is definitely no more than 2,242 nautical miles - which is 2,580 statute miles.

They then added another 827 nautical mile cable to reach Cape Code - so another 951 statute miles...AT MOST.

The distance from Cape Cod to New York has been measured (I'm quite sure) by MANY car odometers along Hwy 95 and comes out to 253 miles - and similarly, Paris to Brest is 364 miles and I'm sure that's been confirmed by large numbers of old-school mechanical odometers too.

So we KNOW that the furthest it could possibly be between NY and Paris is 2,580+951+253+364 = 4,148 miles.  This is clearly not the shortest route, so the true number must be less than this.   Saint-Pierre is about 100 miles North of the ideal Great circle route - so we know that at least 100 miles of cable was wasted in that detour.

But this number does avoid any reliance on any new-fangled technology that scares the bejeezus out of Tom...and it's hard to see how he could argue that it's wrong.

The scary, new technology distance is shorter (no real surprise there) and comes out to be 3,631.16 miles...so the modern approach cannot possibly be inaccurate by more than 517 miles...and allowing for the Saint-Pierre detour, the modern measure agrees to within about 10%.

Since we can be sure that the route the cable took via Newfoundland was not optimal - and the vagiaries of the wiggly roads between Paris/Brest and CapeCod/NewYork  must add considerably to the distance - the precision of the modern measurement is clearly MUCH better than 10%...but that's hard to prove.

[JHelzer]

Please explain how we can know the distance between LA and New York by looking at the arrival times of airplanes without knowing anything about their speed.

We don't care about the distance.
We don't care about the speed of the plane.
All we care about is the average (or perhaps mean depending) time it takes to get from LA to NY by plane.
This can be used as a distance 'replacement' or analogue so long as we simply use the actual times taken.

I don't know how to make it any simpler than what Curious Squirrel is saying here.
I don't care about calculating distances.
I am not using V = D/T  or D = VT

I am making a very simple layout of the earth based on the times that people experience from liftoff to touchdown on commercial airliners.
It is simple.  It is easy.  It will produce a general picture of what the earth looks like.
It will not be precise, it will be an approximate representation.

[altman42]

This won't work.

Lets look at this rationally.  Anyone who has ridden a plane knows that it takes off and then goes to a certain altitude, and during that time accelerates to speed v^c. This takes time t.  During time t, v is increasing from v⁰ to v^c at some rate, which we don't know.  But lets say for the sake of argument- that it's always 30 min to get to altitude and its always 30 min to land, and during that hour speed is always less than v^c.  Lets say this distance traveled during this approximately and hour is constant (which its not, but for ease of calculation) and call it X.  Otherwise we'll have to deal with integrals, and I don't want to do that here.

So in a 10 hour flight, 9 hours are at cruising speed v^c, but in a 4 hour flight only 3 hours are at v^c.  This is 90% and 75% of the flight respectively.  Which means when you compare 2 non-similar lengths, the ratio will be severely skewed.

Next, lets take short flights vs. long flights.  Flights of different lengths usually have different planes, which have different cruising speeds.

So if you want to make a map using only this information and not the speed themselves, then you have to have an adjustment factor, I, to adjust the time by the ratio of speeds between Plane 1 and Plane 2 (v¹/v²).  It's easiest to pick a single base plane and set that as I=1 and compare all the rest to that. So now your times will be comprable.

So, a barely reasonable formula might be ((t-1)*v^c)*I+X. 

Now you also have to account for prevailing wind speed, which will change the speed of the plane- +w for tailwinds and -w for headwinds.  You have to adjust the speed w to account for the fact that it might not be perfectly parallel to the plane, which we can find by taking the angle between the direction of travel and the direction of wind-Theta.

This gives ((t-1)*(v^c)+w cos (theta))*I+X

 Then, you also have to account for general human elements, that might change a flight- usually the planes will go a little faster or slower to make sure that they arrive in a particular time window so that there is a gate available. Your presumption that planes always travel the perfect speed is wrong.  My car has a listed cruising speed of 60mph, but I'll push it to 80mph if I'm late, and slow down to 40mph if the weather is bad.  Planes also have different cruising speeds at different altitudes.  This is because the oxygen content in the air changes and the engine has to maintain sufficient flow through it, etc. etc.   So all of these things together add an error of lets say- extrememly conservatively 10%.

So to find the distance between two seperate line segments since we don't believe in maps or modern technology such as GPS-you want the ratio between two distances which would be sufficient to draw an unscaled map- you can calculate:
((t₁-1*h)*(v₁^c)+w₁ cos (theta₁))*I₁+X/ ((t₂-1h)*(v₂^c)+w₂ cos (theta₂))*I₂+X.

It might seem that X would cancel, but it won't. We also need to adjust that by I because I is the term that adjusts based on v^c.  We can adjust X by dividing by I (since we will cover distance X faster if v^c is faster.  But we also need to adjust X by an additional factor-h that takes into account 2 things- the altitude we are at before we hit v^c, and the time it takes to get there-
 
((t₁-1h)*(v₁^c)+w₁ cos (theta₁))*I₁+(X*(h₂/h₁/I) / ((t₂-1h)*(v₂^c)+w₂ cos (theta₂))*I₂+(X*(h₁/h₂/I)   +/- 10%.

This would give you a minimimally accurate ratio that you can calculate using the information you have at hand.  You can  not do any less, because you are talking about making a map afterall.  Not just guesstimating how far it is.  You could do this all in Excel.  Only from flight aware you also need to grab the type of plane, and maybe the windspeed from there or somewhere else.  The +/- 10% is also critical. 

You also have to remove the additional distance that the planes fly because they think they are travelling along a curved earth.  I've got to get back to work, but you can find the math here- https://math.stackexchange.com/questions/830413/calculating-the-arc-length-of-a-circle-segment

Basically if you fly from Paris to NYC you have to figure out what that distance would be on a round earth- and divide the arc length by the line segment length to come up with a ratio.  This would be a correction factor.  This correction factor, A, grows in significance the longer the distance- to a maximum of pi/2*d where d is the diameter of a supposedly round earth.  Since you are using flights that go across most the world, or at least across the country, this becomes pretty important.  You can find it by multiplying the change in Latitude squared + the change in latitude squared to the 1/2 power (pythagoras' theorom). (ΔLat² + ΔLong²)^(1/2)- thats your round Earth distance in Lat/Long- convert that to miles (since our speeds are in miles)- and then divide that by d.  Thats your Round Earth distance traveled.  To Calculate the Flat Earth Equivalent is tougher.  I'd have to think about that. but it would be:
FEE/RDE * (  ((t₁-1h)*(v₁^c)+w₁ cos (theta₁))*I₁+(X*(h₂/h₁/I) / ((t₂-1h)*(v₂^c)+w₂ cos (theta₂))*I₂+(X*(h₁/h₂/I)  )   +/- 10%.

So, most of the eq. is:

  Flat Earth Eq. / ((ΔLat² + ΔLong²)^(1/2)) * (  ((t₁-1h)*(v₁^c)+w₁ cos (theta₁))*I₁+(X*(h₂/h₁/I) / ((t₂-1h)*(v₂^c)+w₂ cos (theta₂))*I₂+(X*(h₁/h₂/I)  )   +/- 10%.

Just leaving you one piece to find yourself.  You should be able to do it from there.

[altman42]

there should be closed parentheses after the h term before /I in the adjustment term.  It gets hard to read with all the markup it took to document that semi-correctly and it won't let me edit.

[Curious Squirrel]

-math snipped for brevity of reply-

I get where you're coming from here, but once again: Distance is not being calculated here. We're not looking for an incredibly accurate map.
These are the parameters/assumptions:

1) Flight times between two locations are the same within a reasonable margin of error so long as it's the same model plane.
2) The distance between two points doesn't change randomly.
3) Planes will always attempt to fly the shortest distance between two points.
4) Flight times in one direction can be combined with flight times in the other direction for an average flight time within a reasonable margin of error.
5) Flight times can thus be used as a reasonable approximation for distance, and should reveal the shape of the Earth if plotted out.
6) Flight times should not be skewed enough to make a flat Earth appear round, nor a round Earth appear flat.

Now, we'll see how well 1 and 4 turn out for margins of error, but I see nothing wrong with the rest of these otherwise. Once again, no distance in miles or kilometers is being calculated, nor is there an attempt to calculate said distances being made. This is about plotting air flight times onto a map, and seeing what shape the flight times dictate the map to be.

[Ga_x2]

there should be closed parentheses after the h term before /I in the adjustment term.  It gets hard to read with all the markup it took to document that semi-correctly and it won't let me edit.

you could have spared the effort 
The first half of the post is partly taken care of a priori, and partly by the averages. We'll see how those error bars look like. The second half is irrelevant, because no one cares about the actual distances, only the ratio is relevant.
Did you read the thread before writing that wall of formulae? 

[Tom Bishop]

Please tell us the distance between New York and Paris without using a method that assumes the earth is round.

Oh good grief Tom...you really think you can kill the debate with such a ridiculous challenge?   Remember, we're smarter than you are.

In 1878, a 2,242 nautical mile cable was manufactured in England by Siemens Brothers.  The cable was laid in June 1879 between Brest (France) and the island of Saint-Pierre (Newfoundland) by the cable ship "Faraday".

They didn't run out of cable along the way - but history does not recall whether they had any left over.

So we can be quite certain that Brest to Saint-Pierre is definitely no more than 2,242 nautical miles - which is 2,580 statute miles.

They then added another 827 nautical mile cable to reach Cape Code - so another 951 statute miles...AT MOST.

The distance from Cape Cod to New York has been measured (I'm quite sure) by MANY car odometers along Hwy 95 and comes out to 253 miles - and similarly, Paris to Brest is 364 miles and I'm sure that's been confirmed by large numbers of old-school mechanical odometers too.

So we KNOW that the furthest it could possibly be between NY and Paris is 2,580+951+253+364 = 4,148 miles.  This is clearly not the shortest route, so the true number must be less than this.   Saint-Pierre is about 100 miles North of the ideal Great circle route - so we know that at least 100 miles of cable was wasted in that detour.

But this number does avoid any reliance on any new-fangled technology that scares the bejeezus out of Tom...and it's hard to see how he could argue that it's wrong.

The scary, new technology distance is shorter (no real surprise there) and comes out to be 3,631.16 miles...so the modern approach cannot possibly be inaccurate by more than 517 miles...and allowing for the Saint-Pierre detour, the modern measure agrees to within about 10%.

Since we can be sure that the route the cable took via Newfoundland was not optimal - and the vagiaries of the wiggly roads between Paris/Brest and CapeCod/NewYork  must add considerably to the distance - the precision of the modern measurement is clearly MUCH better than 10%...but that's hard to prove.

How do we know that they were not using a Round Earth Coordinate system for measuring those miles out when traveling on their ship?

How do we know that they only brought along the exact amount of cable needed rather than giant spools of it?

How do we know that they did not encounter any issues along the way in early ventures that caused them to revisit their cable laying strategies?

[3DGeek]

How do we know that they were not using a Round Earth Coordinate system for measuring those miles out when traveling on their ship?

The required amount of cable was of course calculated using Round Earth data - probably with a small margin for error - but the actual miles of the stuff that were manufactured must have been measured out in the factory.

What we KNOW is how much they manufactured.

How do we know that they only brought along the exact amount of cable needed rather than giant spools of it?

That's how much they MANUFACTURED - they may have needed less than that - but for 100% sure, they didn't have on yard more than that.  Hence the distance is the MAXIMUM that it could have been.

How do we know that they did not encounter any issues along the way in early ventures that caused them to revisit their cable laying strategies?

Whatever they did, a cable of no more than that length ended up stretching from one side of the atlantic to the other.

I was reading about transatlantic cables in conjunction with a project I was doing...I *think* it was described in "Wiring the World: The Social and Cultural Creation of Global Telegraph Networks" (Columbia Studies in International and Global History) by Simone M. Müller ... but it might have been "A Thread Across the Ocean" - sorry, don't have that one on my bookshelf anymore.

I think both books are on Amazon if you want to get into it further.  Wikipedia probably has something to back this up with the usual small mountain of references.

[JHelzer]

This won't work.

Lets look at this rationally.  Anyone who has ridden a plane knows that ....

Here are two take-aways from this for me.

• You have proved that the error will never  reach as high as 40% for any flight.  This is great news because it means that the flight time data can't make a flat earth appear to be a globe, nor can it make a globe falsely look flat.  I have been asking members of Flat Earth Society to join me in this assertion and you have created a very nice proof for this.  Thank you.
• I will see if it is feasible to limit my flight times to 6 - 8 hr flights.  If that's possible, my error goes down significantly.

[StinkyOne]

Please tell us the distance between New York and Paris without using a method that assumes the earth is round.

Oh good grief Tom...you really think you can kill the debate with such a ridiculous challenge?   Remember, we're smarter than you are.

In 1878, a 2,242 nautical mile cable was manufactured in England by Siemens Brothers.  The cable was laid in June 1879 between Brest (France) and the island of Saint-Pierre (Newfoundland) by the cable ship "Faraday".

They didn't run out of cable along the way - but history does not recall whether they had any left over.

So we can be quite certain that Brest to Saint-Pierre is definitely no more than 2,242 nautical miles - which is 2,580 statute miles.

They then added another 827 nautical mile cable to reach Cape Code - so another 951 statute miles...AT MOST.

The distance from Cape Cod to New York has been measured (I'm quite sure) by MANY car odometers along Hwy 95 and comes out to 253 miles - and similarly, Paris to Brest is 364 miles and I'm sure that's been confirmed by large numbers of old-school mechanical odometers too.

So we KNOW that the furthest it could possibly be between NY and Paris is 2,580+951+253+364 = 4,148 miles.  This is clearly not the shortest route, so the true number must be less than this.   Saint-Pierre is about 100 miles North of the ideal Great circle route - so we know that at least 100 miles of cable was wasted in that detour.

But this number does avoid any reliance on any new-fangled technology that scares the bejeezus out of Tom...and it's hard to see how he could argue that it's wrong.

The scary, new technology distance is shorter (no real surprise there) and comes out to be 3,631.16 miles...so the modern approach cannot possibly be inaccurate by more than 517 miles...and allowing for the Saint-Pierre detour, the modern measure agrees to within about 10%.

Since we can be sure that the route the cable took via Newfoundland was not optimal - and the vagiaries of the wiggly roads between Paris/Brest and CapeCod/NewYork  must add considerably to the distance - the precision of the modern measurement is clearly MUCH better than 10%...but that's hard to prove.

How do we know that they were not using a Round Earth Coordinate system for measuring those miles out when traveling on their ship?

How do we know that they only brought along the exact amount of cable needed rather than giant spools of it?

How do we know that they did not encounter any issues along the way in early ventures that caused them to revisit their cable laying strategies?

Tom, literally EVERYONE uses the round Earth coordinate system because IT WORKS. When are you flat Earthers going to understand this? If we relied on FET, no one would get anywhere over large distances because you can't even come up with a map. Actually, let me rephrase that, you refuse to come up with a map. It is very much on purpose. Once you have a map, you'd see that the Earth actually is a globe.

Yes Tom, they bring GIANT spools of cable. I'm sure they have thousands of miles of it just laying around. I don't know what you do for a living, but in the round world, we don't just buy hundreds of miles of extra cable for the heck of it. Having massive amounts of extra cable = wasted money. Hauling around thousands of pounds of unneeded cable = wasted money.  Further, when you're on the ocean, they can't just overnight you an extra hundred miles of the stuff. These projects are planned out in advance. Economics dictate it.

[TomInAustin]

Please tell us the distance between New York and Paris without using a method that assumes the earth is round.

Oh good grief Tom...you really think you can kill the debate with such a ridiculous challenge?   Remember, we're smarter than you are.

In 1878, a 2,242 nautical mile cable was manufactured in England by Siemens Brothers.  The cable was laid in June 1879 between Brest (France) and the island of Saint-Pierre (Newfoundland) by the cable ship "Faraday".

They didn't run out of cable along the way - but history does not recall whether they had any left over.

So we can be quite certain that Brest to Saint-Pierre is definitely no more than 2,242 nautical miles - which is 2,580 statute miles.

They then added another 827 nautical mile cable to reach Cape Code - so another 951 statute miles...AT MOST.

The distance from Cape Cod to New York has been measured (I'm quite sure) by MANY car odometers along Hwy 95 and comes out to 253 miles - and similarly, Paris to Brest is 364 miles and I'm sure that's been confirmed by large numbers of old-school mechanical odometers too.

So we KNOW that the furthest it could possibly be between NY and Paris is 2,580+951+253+364 = 4,148 miles.  This is clearly not the shortest route, so the true number must be less than this.   Saint-Pierre is about 100 miles North of the ideal Great circle route - so we know that at least 100 miles of cable was wasted in that detour.

But this number does avoid any reliance on any new-fangled technology that scares the bejeezus out of Tom...and it's hard to see how he could argue that it's wrong.

The scary, new technology distance is shorter (no real surprise there) and comes out to be 3,631.16 miles...so the modern approach cannot possibly be inaccurate by more than 517 miles...and allowing for the Saint-Pierre detour, the modern measure agrees to within about 10%.

Since we can be sure that the route the cable took via Newfoundland was not optimal - and the vagiaries of the wiggly roads between Paris/Brest and CapeCod/NewYork  must add considerably to the distance - the precision of the modern measurement is clearly MUCH better than 10%...but that's hard to prove.

How do we know that they were not using a Round Earth Coordinate system for measuring those miles out when traveling on their ship?

How do we know that they only brought along the exact amount of cable needed rather than giant spools of it?

How do we know that they did not encounter any issues along the way in early ventures that caused them to revisit their cable laying strategies?

Had you read the post you would have known the answers to all three questions.   You are really just getting silly now.  Why are you so afraid of a map?

[Tom Bishop]

The required amount of cable was of course calculated using Round Earth data - probably with a small margin for error - but the actual miles of the stuff that were manufactured must have been measured out in the factory.

What we KNOW is how much they manufactured.

Really? How do you KNOW that?

That's how much they MANUFACTURED - they may have needed less than that - but for 100% sure, they didn't have on yard more than that.  Hence the distance is the MAXIMUM that it could have been.

Do you have a source on that? Do you own the manufacturing company?

Whatever they did, a cable of no more than that length ended up stretching from one side of the atlantic to the other.

I was reading about transatlantic cables in conjunction with a project I was doing...I *think* it was described in "Wiring the World: The Social and Cultural Creation of Global Telegraph Networks" (Columbia Studies in International and Global History) by Simone M. Müller ... but it might have been "A Thread Across the Ocean" - sorry, don't have that one on my bookshelf anymore.

I think both books are on Amazon if you want to get into it further.  Wikipedia probably has something to back this up with the usual small mountain of references.

Please provide a source that shows that the cable perfectly matched the Round Earth distance, and not any more and not any less. You seem so forgetful in citing your sources when you make your numerous claims.

[xenotolerance]

The required amount of cable was of course calculated using Round Earth data - probably with a small margin for error - but the actual miles of the stuff that were manufactured must have been measured out in the factory.

What we KNOW is how much they manufactured.

Really? How do you KNOW that?

That's how much they MANUFACTURED - they may have needed less than that - but for 100% sure, they didn't have on yard more than that.  Hence the distance is the MAXIMUM that it could have been.

Do you have a source on that? Do you own the manufacturing company?

Whatever they did, a cable of no more than that length ended up stretching from one side of the atlantic to the other.

I was reading about transatlantic cables in conjunction with a project I was doing...I *think* it was described in "Wiring the World: The Social and Cultural Creation of Global Telegraph Networks" (Columbia Studies in International and Global History) by Simone M. Müller ... but it might have been "A Thread Across the Ocean" - sorry, don't have that one on my bookshelf anymore.

I think both books are on Amazon if you want to get into it further.  Wikipedia probably has something to back this up with the usual small mountain of references.

Please provide a source that shows that the cable perfectly matched the Round Earth distance, and not any more and not any less. You seem so forgetful in citing your sources when you make your numerous claims.

On page 38 of this book there is a list of cables and their lengths. The New York - Paris cable is listed with a length of just over 4000 miles.

It took me <5 minutes of googling to look this up. If you spent half as much energy trying to learn anything as you do on denialism, you might learn anything at all ever.

[Tom Bishop]

The required amount of cable was of course calculated using Round Earth data - probably with a small margin for error - but the actual miles of the stuff that were manufactured must have been measured out in the factory.

What we KNOW is how much they manufactured.

Really? How do you KNOW that?

That's how much they MANUFACTURED - they may have needed less than that - but for 100% sure, they didn't have on yard more than that.  Hence the distance is the MAXIMUM that it could have been.

Do you have a source on that? Do you own the manufacturing company?

Whatever they did, a cable of no more than that length ended up stretching from one side of the atlantic to the other.

I was reading about transatlantic cables in conjunction with a project I was doing...I *think* it was described in "Wiring the World: The Social and Cultural Creation of Global Telegraph Networks" (Columbia Studies in International and Global History) by Simone M. Müller ... but it might have been "A Thread Across the Ocean" - sorry, don't have that one on my bookshelf anymore.

I think both books are on Amazon if you want to get into it further.  Wikipedia probably has something to back this up with the usual small mountain of references.

Please provide a source that shows that the cable perfectly matched the Round Earth distance, and not any more and not any less. You seem so forgetful in citing your sources when you make your numerous claims.

On page 38 of this book there is a list of cables and their lengths. The New York - Paris cable is listed with a length of just over 4000 miles.

It took me <5 minutes of googling to look this up. If you spent half as much energy trying to learn anything as you do on denialism, you might learn anything at all ever.

[xenotolerance]

lol oh man. not sure why I can see it if you can't. attached a snip

distance is in km

[TomInAustin]

The required amount of cable was of course calculated using Round Earth data - probably with a small margin for error - but the actual miles of the stuff that were manufactured must have been measured out in the factory.

What we KNOW is how much they manufactured.

Really? How do you KNOW that?

That's how much they MANUFACTURED - they may have needed less than that - but for 100% sure, they didn't have on yard more than that.  Hence the distance is the MAXIMUM that it could have been.

Do you have a source on that? Do you own the manufacturing company?

Whatever they did, a cable of no more than that length ended up stretching from one side of the atlantic to the other.

I was reading about transatlantic cables in conjunction with a project I was doing...I *think* it was described in "Wiring the World: The Social and Cultural Creation of Global Telegraph Networks" (Columbia Studies in International and Global History) by Simone M. Müller ... but it might have been "A Thread Across the Ocean" - sorry, don't have that one on my bookshelf anymore.

I think both books are on Amazon if you want to get into it further.  Wikipedia probably has something to back this up with the usual small mountain of references.

Please provide a source that shows that the cable perfectly matched the Round Earth distance, and not any more and not any less. You seem so forgetful in citing your sources when you make your numerous claims.

OMG, you take the word of a known con man from 150 years ago and discount the records of a company laying cable.   Very odd man.

[JHelzer]

Setting cable lengths and our abilities to search the internet aside....

Does anyone have anything else to add to the flight time map discussion?

• We have established that care needs to be taken when comparing short flights to long flights because a larger percentage of the flight is take up in ascending and descending from cruising altitude and speed.
• We have established that the purpose of the project is not to calculate distances, but to layout the general size and relative location of continents
• We have established that the margin of error is not great enough to change a flat earth into a globe or to change a globe into a flat earth.